We used to run it in a 'street bike class' which called for a road legal tyre. These came from Yokohama and were really a 180 soft compound slick with a bit of tread cut in. Sometimes we'd change class and pop a full blown Goodyear slick and wheelie bars on ... but we tended to do that with the 'blown' stuff rather than the 'juiced'What section tyre did you have to use to harness 400bhp (at the crank I assume?) through one wheel onto tarmac?

Sorry, everyone but Zippy did kind of ask.
The key to getting 200hp of gas in, is to do it gradually ... we had a system that we could add or subtract hp and alter ignition settings, rev limiters, etc, etc.
A simplified version goes something like this:
Micro-switch on the throttle and another on the clutch. Pull clutch in and the system engages, hold throttle wide open and system arms. You're now sat on the line waiting for the green. The engine will hold itself at whatever revs you've dialed in and 'stutter', ie the ignition will knock out alternate cylinders to prevent engine damage, this would usually be set to between 4k - 6k. This is the rpm you'll leave the start line at.
Light goes green - drop the clutch. The bike will 'launch', revs will go from whatever you're stuttering at to full in under a second. The first wave of gas will hit the motor the second the clutch is released, we'd usually dial between 25% - 40% of our maximum, depending on track conditions.
Over the next few seconds, the amount of gas will increase (the gas and additional fuel are controlled by solenoids that fluctuate until they're permanently open at which point you've reached 100% and your output is being governed by your jet selection in the foggers). We could control the length of time taken to reach maximum and also whether we brought it in 'hard' or 'soft'. As the % of gas increases, the ignition timing retards to compensate (that's something you really try not the get wrong). We'd also run a lock-up clutch that would slip at lower revs to help prevent the tyre breaking free, then if I'd got my sums right, it would be fully locked up by the time we hit the 1/8 mile.
Gear shifts were always by way of air shifter and a great big 'shift light' told you when to hit the button ... no tacho as it wouldn't keep up.